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Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum Formula

GoRadial Velocity in Elliptic Orbit given Radial Position and Angular Momentum Formula

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Radial Velocity of Satellite is the component of its velocity that is directed along the line of sight from an observer on the Earth's surface. Check FAQs

v r = [GM.Earth] \cdot e e \cdot \frac{\sin (θ e)}{h e}

v_r - Radial Velocity of Satellite?e_e - Eccentricity of Elliptical Orbit?θ_e - True Anomaly in Elliptical Orbit?h_e - Angular Momentum of Elliptic Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum Example

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Here is how the Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum equation looks like with Values.

Here is how the Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum equation looks like with Units.

Here is how the Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum equation looks like.

2.5671 = 4E+14 \cdot 0.6 \cdot \frac{\sin (135.11)}{65750}

2.5671km/s = 4E+14m³/s² \cdot 0.6 \cdot \frac{\sin (135.11°)}{65750km²/s}

2.5671 = 4E+14 \cdot 0.6 \cdot \frac{\sin (135.11)}{65750}

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Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum Solution

Follow our step by step solution on how to calculate Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum?

FIRST Step Consider the formula

v r = [GM.Earth] \cdot e e \cdot \frac{\sin (θ e)}{h e}

Next Step Substitute values of Variables

∴

v r = [GM.Earth] \cdot 0.6 \cdot \frac{\sin (135.11°)}{65750km²/s}

Next Step Substitute values of Constants

∴

v r = 4E+14m³/s² \cdot 0.6 \cdot \frac{\sin (135.11°)}{65750km²/s}

Next Step Convert Units

∴

v r = 4E+14m³/s² \cdot 0.6 \cdot \frac{\sin (2.3581rad)}{6.6E+10m²/s}

Next Step Prepare to Evaluate

∴

v r = 4E+14 \cdot 0.6 \cdot \frac{\sin (2.3581)}{6.6E+10}

Next Step Evaluate

∴

v r = 2567.10056776404m/s

Next Step Convert to Output's Unit

∴

v r = 2.56710056776404km/s

LAST Step Rounding Answer

∴

v r = 2.5671km/s

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum Formula Elements

Variables

Constants

Functions

Radial Velocity of Satellite

Radial Velocity of Satellite is the component of its velocity that is directed along the line of sight from an observer on the Earth's surface.

Symbol: v_r

Measurement: SpeedUnit: km/s

Note: Value should be greater than 0.

Formulas to find Radial Velocity of Satellite

Eccentricity of Elliptical Orbit

Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.

Symbol: e_e

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Eccentricity of Elliptical Orbit

True Anomaly in Elliptical Orbit

True Anomaly in Elliptical Orbit measures the angle between the object's current position and the perigee (the point of closest approach to the central body) when viewed from the focus of the orbit.

Symbol: θ_e

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find True Anomaly in Elliptical Orbit

Angular Momentum of Elliptic Orbit

Angular Momentum of Elliptic Orbit is a fundamental physical quantity that characterizes the rotational motion of an object in orbit around a celestial body, such as a planet or a star.

Symbol: h_e

Measurement: Specific Angular MomentumUnit: km²/s

Note: Value should be greater than 0.

Formulas to find Angular Momentum of Elliptic Orbit

Earth’s Geocentric Gravitational Constant

Earth’s Geocentric Gravitational Constant the gravitational parameter for the Earth as the central body.

Symbol: [GM.Earth]

Value: 3.986004418E+14 m³/s²

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other Formulas to find Radial Velocity of Satellite

Go Radial Velocity in Elliptic Orbit given Radial Position and Angular Momentum

v r = \frac{h e}{r e}

Other formulas in Elliptical Orbit Parameters category

Go Eccentricity of Elliptical Orbit given Apogee and Perigee

e e = \frac{r e,apogee - r e,perigee}{r e,apogee + r e,perigee}

Go Angular Momentum in Elliptic Orbit Given Apogee Radius and Apogee Velocity

h e = r e,apogee \cdot v apogee

Go Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity

r e,apogee = \frac{{h e}^{2}}{[GM.Earth] \cdot (1 - e e)}

Go Semimajor Axis of Elliptic Orbit given Apogee and Perigee Radii

a e = \frac{r e,apogee + r e,perigee}{2}

How to Evaluate Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum?

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum evaluator uses Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit to evaluate the Radial Velocity of Satellite, Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum formula is defined as a measure of the velocity of an object in an elliptical orbit around a central body, providing insight into the object's motion and position in the orbit. Radial Velocity of Satellite is denoted by v_r symbol.

How to evaluate Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum using this online evaluator? To use this online evaluator for Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum, enter Eccentricity of Elliptical Orbit (e_e), True Anomaly in Elliptical Orbit (θ_e) & Angular Momentum of Elliptic Orbit (h_e) and hit the calculate button.

FAQs on Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum

What is the formula to find Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum?

The formula of Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum is expressed as Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit. Here is an example- 0.002567 = [GM.Earth]*0.6*sin(2.3581143523691)/65750000000.

How to calculate Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum?

With Eccentricity of Elliptical Orbit (e_e), True Anomaly in Elliptical Orbit (θ_e) & Angular Momentum of Elliptic Orbit (h_e) we can find Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum using the formula - Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit. This formula also uses Earth’s Geocentric Gravitational Constant and Sine (sin) function(s).

What are the other ways to Calculate Radial Velocity of Satellite?

Here are the different ways to Calculate Radial Velocity of Satellite-

Radial Velocity of Satellite=Angular Momentum of Elliptic Orbit/Radial Position in Elliptical Orbit

Can the Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum be negative?

No, the Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum, measured in Speed cannot be negative.

Which unit is used to measure Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum?

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum is usually measured using the Kilometer per Second[km/s] for Speed. Meter per Second[km/s], Meter per Minute[km/s], Meter per Hour[km/s] are the few other units in which Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum can be measured.

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